What is the limit as x approaches 0+of 1/x*sin(1/x) ?

The limit as x approaches 0+of 1/x*sin(1/x) is diverges

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limit as x approaches 0+of 1/x*sin(1/x)

x \to 0 + lim (\frac{1}{x} \cdot sin (\frac{1}{x}))

diverges

Solution steps

x \to 0 + lim (\frac{1}{x} sin (\frac{1}{x}))

Simplify

\frac{1}{x} sin (\frac{1}{x}) : \frac{sin ( \frac{1}{x} )}{x}

= x \to 0 + lim (\frac{sin ( \frac{1}{x} )}{x})

Apply Limit Divergence Criterion:

diverges

= diverges

\frac{\partial}{\partial x} (4 ln (x y))

x^{3} - 6 x^{2} - 34 x + 40, at x = 6

\int - k x d x

\int \frac{1}{x ( x + 1 )} d x

x \to 0 lim (\frac{( x + 5 )}{3 x})

What is the limit as x approaches 0+of 1/x*sin(1/x) ?
The limit as x approaches 0+of 1/x*sin(1/x) is diverges